It is known that ground surfaces of workpieces, in particular of roller bearings, are finished in a further work step wherein, for one, the roughness of the surface is reduced, and furthermore accuracy as to shape and dimension is increased. As a rule, up to 6 .mu.m of material are removed during this finishing process, in special cases even 50 .mu.m and more. Flat surfaces are worked by means of a flat finishing block, which is used in the plane of the surface. Curved surfaces are also worked with a finishing block, wherein the work surfaces of the finishing block in this case are not flat, but matched to the curvature of the surface to be worked. The block is pivoted during the treatment, so that at all times it rests flat against the workpiece to be treated, or respectively on its surface to be treated. To this end the finishing block is clamped in a pivoting device, whose pivot axis is located in the center of curvature of the surface to be treated. It has been shown that only a limited number of workpieces can be treated by means of such devices. Workpieces with a slight curved surface, i.e. with surfaces whose radius of curvature is very large, cannot be treated with such devices, since as a rule the pivot arm for pivoting the finishing block is too short. This applies in particular to angularly adjustable movable bearings and large spherical roller bearings.
CNC treatment machines are furthermore known, by means of which treatment tools, for example drills, turning chisels, and the like can be displaced in space. However, such tools have point-shaped or line-shaped cutting surfaces, so that, although the angular position of the tool with respect to the workpiece is determined by the effective tool side rake, this effective tool side rake can be variable over relatively large ranges. Machines of this type are not suitable for tools which treat the workpiece not at points or along lines, but in a planar manner, namely by means of a finishing block. In relation to the tool, this finishing block must not only be exactly positioned in the X, Y plane, but also in its angular position, so that the cutting surface of the finishing block at all times rests flat on the surface of the workpiece to be treated.